The complex index of refraction of substances with respect to X-rays is normally expressed as n=1-.delta.-i k (where .delta. and k are real numbers). The values of .delta. and k are usually extremely small compared to 1, and the imaginary part k of the refractive index expresses X-ray absorption by the substance. For this reason, lenses made for refraction of, for example, visible light normally cannot be used for refracting X-rays. Also, because .delta. and k are extremely small, surface reflectance of the substance is extremely low.
Certain X-ray-reflecting surfaces comprise a large number of layers of substances exhibiting as high an interface-amplitude reflectance as possible. The thickness of each layer can be adjusted according to optical interference theory. The number of layers can be, e.g., in the hundreds, with matching of the phase of each reflected wave. Such a reflective surface can be made by alternately layering, on a suitable substrate, a substance exhibiting a refractive index for the X-ray wavelength used that is not significantly different from the refractive index (unity) of a vacuum, and a substance exhibiting a refractive index that is significantly different from unity.
Conventional membranes used in multi-layer X-ray-reflecting mirrors include W/C (tungsten/carbon), Mo/C (molybdenum/carbon), and Mo/Si (molybdenum/silicon). Such layers can be formed using techniques for forming thin films such as sputtering, vacuum evaporation, and CVD (chemical vapor deposition).
The availability of multi-layer reflecting mirrors that can reflect X-rays incident to the mirror at a zero angle of incidence allows an X-ray optical system to be made that exhibits less aberration than exhibited by systems in which the X-rays are incident on reflective surfaces at a highly skewed angle of incidence (e.g., at angles of incidence resulting in total reflection).
A multi-layer X-ray-reflecting mirror normally exhibits a wavelength selectivity, in which X-rays are reflected strongly only when the Bragg formula is satisfied: 2d sin .theta.=n .lambda., where d is the period length of the multiple layers, .theta. is the angle of incidence, and .lambda. is the wavelength of the X-ray.
Among such multi-layer reflective surfaces, certain Mo/Si multi-layer structures exhibit a high reflectance for X-rays on the long-wavelength side of silicon L absorption edges (.lambda.=12.6 nm).
Grazing incidence mirrors can also be used as reflecting optical elements for X-rays. A grazing incidence mirror has a high reflectivity only at a small grazing angle smaller than a critical angle .theta..sup.c (for .lambda.=10 nm, the critical angle .theta..sup.3 is about 20.degree. or less). Such mirrors cannot be used in situations of near normal incidence. A multilayer mirror can be used at any incidence angle including normal incidence. Windt and Waskiewicz, "Multilayer Facilities Required for Extreme-Ultraviolet Lithography," J. Vac. Sci. Technol. B12(6):3826 (1994).
Such X-ray mirrors are conventionally used in X-ray telescopes and X-ray laser resonators. X-ray-reflecting mirrors comprising multiple Mo/Si layers have potential uses in reduction projection-lithography systems that utilize "soft" X-rays (i.e., X-rays of relatively long wavelength, low energy, and little penetrative power).
Mo/Si multi-layer reflecting mirrors exhibiting high reflectance for X-rays are conventionally made using a sputtering technique involving a plasma. Unfortunately, thin films made by sputtering generally exhibit internal stresses arising from compression. Such stresses are typically caused by a "peening" effect of high-speed particles (positive ions and neutral particles) in the plasma, as described in Kinbara, Sputtering Phenomena, Tokyo University Press, 1984.
A multi-layer mirror structure having internal stress typically exhibits substantial warping of the reflective surface. Such warping generates wave-surface aberrations in optical systems comprising such mirrors; such aberrations significantly degrade the optical performance of such systems.
Various techniques have been evaluated to reduce the internal stress in Mo/Si multi-layer membranes. For example, certain stresses apparently can be controlled by varying the thickness ratios of the molybdenum and silicon layers. Nguyen et al., OSA Proceedings On Extreme Ultraviolet Lithography, Vol. 23, p. 56, 1995. Another approach is to change the bias voltage on the substrate during formation of the layers by sputtering. Nakajima et al., Vacuum 37(1): 10-16, 1994. Yet another approach is to vary the applied high-frequency electrical power when applying the layers. Haga et al., 57.sup.th Applied Physics Conference Scientific Lecture Meeting, Abstract 7p-W-1, p. 495 (1996). Yet another approach is to impose a heat stress to the structure by elevating the temperature of the substrate when applying the layers. Wasa et al., 56.sup.th Applied Physics Conference Scientific Lecture Meeting, Abstract 26a-C-5, p. 491 (1995). Unfortunately, application of such techniques provides no real understanding of the true origin of the stresses and how they can be reliably controlled. Thus, whether or not stresses are present in a particular X-ray mirror is unpredictable, and attempts to reduce the stress after manufacture can lead to unexpected and unwanted consequences such as loss of reflectance.